This paper presents a functional framework to study diverse theories of poverty in the current literature. Because of the complex nature of different schools of thought on poverty, one needs a meta-graph that can relate element in the poverty domain of a function to elements in the egalitarian range of the function. This paper presents such a framework that can compare and contrast different theories of poverty. Two novelties of the paper are dynamic analyses for a group of countries, and a correspondence relationship that allows us to look for invariant relationships in models of poverty. The former applies a new dynamic principle in economics, and the latter fills a gap in the literature identified by the Nobel Laureate Amartya Sen’s theory of poverty.